A few questions on Quantum mechanics

[TheDude710]

Hi all, I am doing quantum stuff in my physics class right now and have a few question that I would like to know the answers to...

1) A particle has wave proporties that relate to the probability of where it exists. I guess my question is how do particles move? Like can they exist anywhere that their wave function says at any specific time? Like can a particle jump from on place to somewhere else miles away?

2) With photons, the E&M fields are waving but does do photons also have a probability wave function?

3) In quantum theory, how is motion of a particle explained?

Any other information about basic quantum theory would be great to.

 

[humanino]

1) A particle is described byh a superposition of plane waves. Those plane waves are well located in momentum space, but not at all in position space. Only the sum (superposition) of the plane waves gives a correct representation of the particle. That is a wave packet. Now a wave packet is non zero only in a limited region, whether in position or momentum space. What is called tunneling effect, is when a particle, as you put it "jump from on place to somewhere else miles away". It occurs if the extension of the wave packet goes through a physically forbidden region (typically a region with high potential). The particle can jump from one side to the other side because the wave packet is actually on both sides.

2) The electromagnetic vector potential "A" might be interpreted as the wave function for the photon. But one should only apply this prescription in momentum space. You do not expect a photon to be at a particular position in space because time cannot flow for him. Since his clock is desperatly stucked at zero, the photon can explore an infinite amount of space, but cannot remember it, or something like that.

3) Not explained, preferably described... This is a very general question, and raises answers at many different level. I would say : a free particle is guided by its wave, which kind of sniffs the best path to follow. This is a very old-fashionned viewpoint, but still I like it.

 

[HallsofIvy]

Yes, a particle can be observed to be at any place where the wave function is non-zero because that means a not-zero probability of being observed there! Yes, another observation of that same particle might find it miles away (if the wave function extends that far). However, talking about the particle "jumping" from one place to another implies that you are thinking of the particle as "existing" at some point even when you are not observing it. That is not what happens. One can only think of a particle as having an existence AT a specific point WHILE it is being observed.

As Humanino said, in effect, the electro-magnetic wave IS the wave function for a photon.

A particles wave function covers "all possible paths", some having greater probability than others. Once again, quantum theory says nothing about where the particle is between observations and, indeed, declares such a question meaningless.

 

[ZapperZ]

Hi all, I am doing quantum stuff in my physics class right now and have a few question that I would like to know the answers to...

1) A particle has wave proporties that relate to the probability of where it exists. I guess my question is how do particles move? Like can they exist anywhere that their wave function says at any specific time? Like can a particle jump from on place to somewhere else miles away?

2) With photons, the E&M fields are waving but does do photons also have a probability wave function?

3) In quantum theory, how is motion of a particle explained?

Any other information about basic quantum theory would be great to.

To add to the already two very good answers that you received here, I would like to say that this is a terrific example on how our classical ideas have "corrupted" our view of the physical world. Anyone beginning their studies in QM may want to consider this.

When you ask the question "how does a particle move?", you are ALREADY assuming that there is the ability to know the exact location of a particle over a series of time. This is a purely classical notion. This is but one example on why there are questions that simply either makes no sense or cannot be answered in QM. While the time evolution of a wave function tells you how all the properties associated with that particle changes with time AFTER A SINGLE MEASUREMENT, it doesn't tell you where that particle in going to be after you make a series of measurement. This is because what property you measure and how you measure it affect the system. After that first measurement, you need a new set of wavefunction to describe the new system. The original wavefunction may no longer be appropriate for the new system.

Secondly, to know how a particle move requires that you know both position and momentum with classical accuracy. These are the two information in classical mechanics that are required to completely describe the dynamics of the system. Again, these information are just not available with the same degree of accuracy in QM.

Thirdly, the superposition of eigenstates in QM, as illustrated in the Schrodinger Cat thought experiment IS, as far as the Copenhagen Interpretation is concerned, as "real" as anything. The particle doesn't "jump" from one location to another. The particle occupies ALL the position available to it simultaneously, up to the point where you make a definite position measurement! That is what made QM so difficult to accept by a lot of people. This superposition has been clearly verified experimentally in many SQUID experiments and by chemists without them knowing it (I have given the example of H2 molecule and the bonding-antibonding state in an earlier string).

The moral of the story here is that when you ask a question about the physical property of a system, you may need to look at your question and figure out if you are forcing our classical prejudice into the system. Both QM and Special/General Relativity have shown that a lot of things we take for granted can have different definitions outside our classical world. Most of us who have studied QM in detail are humbled by this realization.

Zz.

 

[humanino]

Is there not two level of discussion here : 1) and 3) indeed raise broad questions about the nature of movement by itself. HallsofIvy and ZapperZ, you gave very accurate answers on that level. But question 2) is especially dedicated to the photon, and we know massless particles must be something very far from our conceptions. I mean : the same must occur for the graviton, right ? One shoukd be able to construct a momentum-localized wavefunction for the graviton, but one should fail in attempting to localize the graviton in position space ?

 

[ZapperZ]

Is there not two level of discussion here : 1) and 3) indeed raise broad questions about the nature of movement by itself. HallsofIvy and ZapperZ, you gave very accurate answers on that level. But question 2) is especially dedicated to the photon, and we know massless particles must be something very far from our conceptions. I mean : the same must occur for the graviton, right ? One shoukd be able to construct a momentum-localized wavefunction for the graviton, but one should fail in attempting to localize the graviton in position space ?

I don't think I made any attempt to address Question #2, mainly because I was too lazy to interpret the question. :)

The problem with addressing questions about photons is that to what extent do you STOP? Is it sufficient to say that in "conventional" QM, photons are only described by its interactions with matter, per your explanation of the vector potential in the Hamiltonian? Or do we have to invoke QED into the picture and run the risk of getting out a rather convoluted explanation? I haven't thought of which one is better, so I skipped that part.

Does that I mean I still get my partial credit?

Zz.

 

[yifan]

How does probability relate to that wave length is momentum over plank constant?

 

[alexepascual]

From what I understand about QM (not much) , the following could be said:

(1) After observing a particle at a particular location, if we make another observation soon after, it will necessarily be located very close to where we found it the first time. If we observe it repeatedly, what we get is something close to a classical trajectory, except that there may be changes in the momentum produced by the observations. The particle could never be observed to jump from one place to "miles away".

(2) Quantum tunneling occurs at very short distances as the probability decays exponentially as we move through the barrier.

Are the above correct?

Are you guys in favor of the Copenhagen school (or interpretation?)
-Alex-

 

[Fliption]

The particle occupies ALL the position available to it simultaneously, up to the point where you make a definite position measurement!

My question is "what do we mean when we say 'measurement'?". What classifies as a measurement? There seem to be two different notions being talked about here about what a measurement does. The first one, that I've seen several times, is the implication that a measurement physically interferes with the particle and initiates a new wave function. This conjures up images of billiard balls bouncing into one another and the very act of physically measuring an object automatically means that the object has moved. This seems no different from classical physics to me.

The second notion, I have quoted above, is implying that the act of measurement is actually causing a particle that occupies all positions in the wave function simultaneously to suddenly choose a single position. This is definitely NOT classical physics. Is this sort of behaviour happening because of a simple physical interference that we label "measurement"? If so then when would particles ever be in a superposition because it seems physical interferences would happen all the time? If this is not the case and physical interference alone is not what collapses the WF, then what makes a "measurement" so special? Is there something more fundamental here that our language isn't communicating?

 

[jcsd]

Fliption the scond notion is the correct one. You've hit on something called the 'measurement problem', because though the act of measuremnt plays an important rukle in quantum mechanics it isn't an easy at all to define. The best expalbntion for years was that a measuremnt was an irrevrisble changhe in a system, nowdays the phenomena of decohernce has solved the measuremnt problem for many:

http://plato.stanford.edu/entries/qm-decoherence/

 

[Fliption]

Fliption the scond notion is the correct one. You've hit on something called the 'measurement problem', because though the act of measuremnt plays an important rukle in quantum mechanics it isn't an easy at all to define. The best expalbntion for years was that a measuremnt was an irrevrisble changhe in a system, nowdays the phenomena of decohernce has solved the measuremnt problem for many:

http://plato.stanford.edu/entries/qm-decoherence/

Decoherence seems to say that it is physical interaction with the environment that causes collapse. But is this consistent with this study?

An unobserved quantum entity is said to exist in a "coherent superposition" of all the possible "states" permitted by its "wave function." But as soon as an observer makes a measurement capable of distinguishing between these states the wave function "collapses", and the entity is forced into a single state.
Yet even this deliberately abstract language contains some misleading implications. One is that measurement requires direct physical intervention. Physicists often explain the uncertainty principle in this way:in measuring the position of a quantum entity, one inevitably blocks it off its course, losing information about its direction and about its phase, the relative position of its crests and troughs.


Most experiments do in fact involve intrusive measurements. For example, blocking one path or the other or moving detectors close to the slits obviously disturbs the photons passage in the two-slit experiment as does placing a detector along one route of the delayed-choice experiment. But an experiment done last year by Mandel's team at the University of Rochester shows that a photon can be forced to switch from wavelike to particlelike behaviour by something much more subtle than direct intervention.
The experiment relies on a parametric down-converter an unusual lens that splits a photon of a given energy into two photons whose energy is half as great. Although the device was developed in the 1960s, the Rochester group pioneered its use in tests of quantum mechanics. In the experiment, a laser fires light at a beam splitter. Reflected photons are directed to one down - converter, and transmitted photons go to another down-converter. Each down-converter splits any photon impinging on it into two lower-frequency photons one called the signal and the other called the idler. The two down-converters are arranged so that the two idler beams merge into a single beam. Mirrors steer the overlapping idlers to one detector and the two signal beams to a separate detector.


This design does not permit an observer to tell which way any single photon went after encountering the beam splitter. Each photon therefore goes both right and left at the beam splitter, like a wave, and passes through both down-converters, producing two signal wavelets and two idler wavelets. The signal wavelets generate an interference pattern at their detector. The pattern is revealed by gradually lengthening the distance that signals from one down - converter must go to reach the detector. The rate of detection then rises and falls as the crests and troughs of the interference wavelets shift in relation to each other, go in and out of phase.

Now comes the odd part. The signal photons and the idler photons, once emitted by the down-converters, never again cross paths; they proceed to their respective detectors independently of each other. Nevertheless, simply by blocking the path of one set of idler photons, the researchers destroy the interference pattern of the signal photons. What has changed?
The answer is that the observer's potential knowledge has changed. He can now determine which route the signal photons took to their detector by comparing their arrival times with those of the remaining, unblocked idlers. The original photon can no longer go both ways at the beam splitter, like a wave, but must either bounce off or pass through like a particle.

http://www.fortunecity.com/emachines/e11/86/qphil.html

This article goes on to describe how an "eraser" can be designed with this experiment which actually introduced even more evironmental disruptions and the system goes from a collapsed state to a quantum state again! The exact opposite of what decoherence would claim. The difference is that the experiment additions "erase" information. So the whole point seems to be correlating collapse to the "potential for knowledge" and not "physical interaction with the environment".

This is why I aked the question earlier about how measurement is defined. So many people talk about it as if they know but it doesn't seem so clear cut to me.

 

[jcsd]

Decoherence seems to say that it is physical interaction with the environment that causes collapse. But is this consistent with this study?




http://www.fortunecity.com/emachines/e11/86/qphil.html

This article goes on to describe how an "eraser" can be designed with this experiment which actually introduced even more evironmental disruptions and the system goes from a collapsed state to a quantum state again! The exact opposite of what decoherence would claim. The difference is that the experiment additions "erase" information. So the whole point seems to be correlating collapse to the "potential for knowledge" and not "physical interaction with the environment".

This is why I aked the question earlier about how measurement is defined. So many people talk about it as if they know but it doesn't seem so clear cut to me.

The wave function does not collapse and 'un-collapse' in the eraser experiment it reamains in a superposed state. Also all it's worth noting these experiments are finally tuned to prevent unwanted decoherence from occurring.

 

[shrumeo]

There was an article in a recent Science where a team used a matter beam of C70. They took a sample of C70 (the fullerene) and vaporized it sending it as a beam through an apparatus, I can't remember if it was just a 2-slit kind of thing, but something to that effect. At "lower" temperatures the beam showed interference patterns and wavelike properties and whatnot, but above a certain critical temperature, there was decoherence and the beam acted particle like. So they proved that coherence can even happen for large molecules and that decoherence would only happen with a sufficient amount of "interaction." Justthought the article was cool. I'll try to find a link to it.

 

[shrumeo]

Ah, well here is a synopsis. If you have access you can link to the actual article and download it.

http://www.sciencemag.org/cgi/content/full/292/5521/1471?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&fulltext=C70&searchid=1085095862385_9859&stored_search=&FIRSTINDEX=0

 

[Fliption]

The wave function does not collapse and 'un-collapse' in the eraser experiment it reamains in a superposed state. Also all it's worth noting these experiments are finally tuned to prevent unwanted decoherence from occurring.

I don't understand what you mean. The whole point of the "eraser" was to show that taking the potential for knowledge away caused a different result. The only result that matters in these experiements is whether the wave function collapses or not. What do you mean it stays in a superposed state?

Also, I don't interpret the setup of the experiment to be to eliminate decoherence specifically(decoherence isn't even mentioned). I just saw it as a way to eliminate as many variables as possible so that the real reason collapse happens can be isolated. Just seems like proper protocol for a good science experiment.

 

[jcsd]

I don't understand what you mean. The whole point of the "eraser" was to show that taking the potential for knowledge away caused a different result. The only result that matters in these experiements is whether the wave function collapses or not. What do you mean it stays in a superposed state?

You said in your last post that the quantum earser gooes from a collapses and goes to qaunum state again it doesn't it stays superposed until it is measured.

Also, I don't interpret the setup of the experiment to be to eliminate decoherence specifically(decoherence isn't even mentioned). I just saw it as a way to eliminate as many variables as possible so that the real reason collapse happens can be isolated. Just seems like proper protocol for a good science experiment.

Decohernce is always a problem, any experiment of this type must elimnate unwanted effects caused by decoherence.

 

[Fliption]

You said in your last post that the quantum earser gooes from a collapses and goes to qaunum state again it doesn't it stays superposed until it is measured.

I'm not sure you're understanding what my point is. The experiment is set up in such a way that it is the measurement. The whole idea of the experiment is that sometimes an interference pattern results and sometimes it does not. You are saying that the difference is that a "measurement is taking place" but I'm trying to get at what that really means. What really is the difference in the two results? What is a measurement? The conclusion from this experiment is that it is the "potential for knowledge" that makes the interference pattern go away; not "interaction with the environment".

 

[alexepascual]

This is the way I see it:
I think decoherence is compatible with the interpretation that collapse implies a change in our knowledge or the "possibility to know".
Quantum non-demolition experiments show that it is not necessarily that you physically disturb the thing when you measure. Just choosing one of the possible outcomes represents a measurement. But how and when is that choice made? Decoherence explains that process.
If you could isolate "Schrodinger's cat" inside the box, so that there is no "information" leaked, then the cat would actually be in a superposition.
But in reality, for large objects like a cat, there is interaction with the environment. If we adopt the "many worlds" interpretation, we could accept that the cat is still in a superposition, but that correlations have been established with the surrounding environment (entanglement).This implies that the environment is now also in a superposition, and correlations have been established between the cat and the environment. The live cat is correlated to one version of the environment, and the dead cat to another.
We could interpret this by saying that there is a "permanent record" in the environment about the state of the cat, which would be compatible with Copenhagen. Or we could say that we as observers are also in a superposition that is entangled with the environment and the cat (many worlds interpretation)
Don't they say there are many ways to skin a cat?

On the mathematical side, I think decoherence deals with the fact that as you can't keep track of the state of the evironment, when you describe the state of the cat with a density operator, the off-diagonal elements become zero, leaving only the different possibilities (dead, alive) in the diagonal but without any phase relations, which implies they are not a superposition but a mixture (the cat is dead or it is alive, not both, but you just don't know)